A diving bell has an air space of 3.2 m³ when on the deck of a boat. What is the volume of the air space when the bell has been lowered to a depth of 50. m? Take the mean density of sea water to be 1.025 g cm^-3 and assume that the temperature is the same as on the surface.

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1 m³

A sample of 4.1 mol O₂ (C^o_p,m = 29.355 J K^-1 mol^-1) is originally confined in 32 dm³ at 270 K and then undergoes adiabatic expansion against a constant pressure of 600 Torr until the volume has increased by a factor of 3.0. Calculate q, w, ΔU, ΔT, and ΔH. (The final pressure of the gas is not necessarily 600 Torr.)
q

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1 kJ
w

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2 kJ
ΔU

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3 kJ
ΔT

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4 K
ΔH

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5 kJ

Calculate the change in Gibbs energy of 20. g of ethanol (mass density 0.789 g cm^-3) when the pressure is increased isothermally from 1 atm to 2991 atm. (Refer to Table 2.8.)

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1 kJ

The molar volume of a certain solid is 161.0 cm³ mol^-1 at 1.00 atm and 350.05 K, its melting temperature. The molar volume of the liquid at this temperature and pressure is 163.3 cm³ mol^-1. At 100. atm the melting temperature changes to 350.56 K. Calculate the enthalpy of fusion of the solid.

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1 J K^-1 mol^-1
Calculate the entropy of fusion of the solid.

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2 kJ mol^-1

Consider a container of volume 4.4 dm³ that is divided into two compartments of equal size. In the left compartment there is nitrogen at 1.0 atm and 32°C; in the right compartment there is hydrogen at the same temperature and pressure. Calculate the Gibbs energy and entropy of mixing when the when the partition is removed. Assume the gases are perfect.
Δ_mixG

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1 kJ
Δ_mixS

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2 J K^-1

It is found that the boiling point of a binary solution of A and B with x_A = 0.6589 is 88°C. At this temperature the vapor pressures of pure A and B are 128.0 kPa and 50.65 kPa, respectively.

Calculate the zero-point energy of a harmonic oscillator consisting of a particle of mass 2.21 10^-26 kg and force constant 144 N m^-1.

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1 J

Many biological electron transfer reactions, such as those associated with biological energy conversion, may be visualized as arising from electron tunnelling between protein-bound co-factors, such as cytochromes, quinones, flavins, and chlorophylls. This tunnelling occurs over distances that are often greater than 1.0 nm, with sections of protein separating the electron donor from acceptor. For a specific combination of donor and acceptor, the rate of electron tunnelling is proportional to the transmission probability, with κ 7 nm^-1 (Use the equations given below.). By what factor does the rate of electron tunnelling between two co-factors increase as the distance between them changes from 2.0 nm to 1.7 nm?

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1

Stern-Gerlach splittings of atomic beams are small and require either large magnetic field gradients or long magnets for their observation. For a beam of atoms with zero orbital angular momentum, such as H or Ag, the deflection is given by x = ±(μ_BL²/4E_K)dB/dz, where μ_B is the Bohr magneton, L is the length of the magnet, E_K is the average kinetic energy of the atoms in the beam, and dB/dz is the magnetic field gradient across the beam.

Select the symmetry elements for the following molecules and the point groups to which they belong.

How many normal modes of vibration are there for H₂O?

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1

A radical containing two equivalent protons shows a three-line spectrum with an intensity distribution 1:2:1. The lines occur at 330.2 mT, 332.5 mT, and 334.8 mT. What is the hyperfine coupling constant for the proton?

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1 mT
What is the g-value of the radical given that the spectrometer is operating at 9.311 GHz?

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2